Why does my model deform so badly when I'm trying to animate it?
For a leg :

You have the leg itself, and a cloth, and the thickness of the cloth. Your problem lies in the inside part of the cloth that is not well vertex-weighted, and then not following the bone's movement.

cloth thickness



Cloth partially deformed



vertex weight of the cloth (1 bone selected)



What I suggest : Delete non-visible vertices (leg hidden by cloth, inside of cloth). As they won't be needed for render anyway, they're useless.

What you can do if you need to keep everything like that : Paint vertex weights (in weight paint mode) or at least assign the parts that need to move to the good vertex group

Weight paint mode



manually assign vertices to a vertex group